Exercise 1: Random walk
Fair use
This problem is adapted from Exercise 37 of Langtangen’s “A Primer on Scientific Programming with Python”.
Simulating gas particles in a closed space is something you can do with a Monte Carlo type simulation – simulate a period of time (using a loop) and “move” particles around
(change values for (x, y) coordinates) for each unit of time. This kind of simulation is called a “random walk”.
Download the file randomwalk.py. This implements a Monte Carlo simulation for a random 2-dimensional walk. It uses numpy arrays, but it does not use them idiomatically.
Your task for this exercise is to change this program to use numpy arrays idiomatically. That is, the block
for i in range(np):
direction = random.randint(1, 4) if direction == NORTH: ypositions[i] += 1 elif direction == SOUTH: ypositions[i] -= 1 elif direction == EAST: xpositions[i] += 1 elif direction == WEST: xpositions[i] -= 1 should be rewritten to use numpy arrays of random integers.
Challenge: multidimensional arrays
Rewrite the code so that (x, y) coordinates are represented with a 2-dimensional numpy array. Here’s how you can start:
coords = np.zeros(shape=(np, 2)) # xpositions = numpy.zeros(np)
# ypositions = numpy.zeros(np)
Remember that you can index entire columns of a 2-dimensional array by using the notation [:,n] to get the nth column.
Super challenge: no loops
Rewrite the code so that it has no loops. You’ll need to think in 3 dimensions to accomplish this.
Answer some question first:
1. Can you simulate time without loops?
2. Each unit of time depends on the unit of time before it. Can different matrices in a 3-dimensional numpy array depend on each other?
If you can answer “yes” to both of these questions, then proceed!
